System and method to control radial delta temperature

ABSTRACT

A system and method of minimizing stress related to the ramp rate of a variable by limiting the ramp rate as a function of the current value of the variable is provided. More specifically, the present invention provides a system and method of maintaining the radial delta temperature of a semiconductor substrate or other heated body below the crystal slip curve by dynamically controlling the temperature ramp rate during processing.

CROSS REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional ApplicationSerial No. 60/274,532, filed Mar. 8, 2001, and to copending U.S. patentapplication Ser. No. 10/068,127 which was filed on Feb. 6, 2002 thedisclosures of both of which are hereby incorporated by reference intheir entirety.

FIELD OF THE INVENTION

[0002] The present invention relates generally to a system and method ofminimizing the stress related to the ramp rate of a control variableduring a manufacturing process such as, for instance, the temperature ofa semiconductor substrate or wafer during processing of the substrate.More specifically, the present invention provides an enhanced system andmethod of maintaining the radial delta temperature (RDT) of a waferduring processing below an excess thermal stress curve by controllingthe temperature ramp rate during processing. In the semiconductorindustry, it is desirable to obtain temperature uniformity in thesubstrate during temperature cycling of the substrate. Temperatureuniformity provides uniform process outputs on the substrate, such aslayer thickness, resistivity, and junction depth, for temperatureactivated steps including film deposition, oxide growth and diffusion ofdopants. In addition, temperature uniformity in the substrate isnecessary to prevent thermal stress-induced wafer damage such aswarpage, defect generation and crystal structure “slip.”

BACKGROUND OF THE INVENTION

[0003] Manufacturing and other processing systems typically involvechanging the value of one or more control variables, including but notlimited to temperature, pressure, gas flow rates, concentration,tension, voltage, applied force, and position. The rate at which acontrol variable is changed from a starting value to an ending value isthe ramp rate or first derivative of that variable, known generically asthe ramp rate. For instance, the ramp rate or first derivative ofposition with regards to time (such as dx/dt) is velocity. It is oftendesirable to minimize stresses to which equipment and/or products areexposed during a process. Excess stress can lead to reduced efficiencyof a process or to premature failure of equipment or products. In manysystems, stresses are a function of the ramp rate of one or more controlvariables. The ramp rate may be reduced to maintain stress below anacceptable threshold. However, unnecessarily severe ramp rate limits arealso undesirable because they slow process throughput. An illustrativeexample of this concept is drawn from semiconductor processing systems.It should be noted, however, that ramp-rate related problems are notunique to the application discussed in detail herein. Rather, theexamples are meant to be merely illustrative and not limiting in anyway.

[0004] An important aspect in the manufacture of semiconductors andintegrated circuits is the temperature variations and values thatsemiconductor wafers are subjected to during processing. Two importantlimitations apply to heating and cooling of semiconductor wafers: 1)acceleration and deceleration of the temperature ramp rate cannot occurmore rapidly than the thermal inertia of the wafer will permit and 2)the temperature difference between the center and edge of a wafer shouldbe kept sufficiently small to prevent thermal expansion damage to thewafer. Thermal inertia describes the resistance of a mass toinstantaneously jumping from a steady-state temperature or zero ramprate state to a finite non-zero ramp rate and back to steady stateagain. Real objects are incapable of the instantaneous and infinite“acceleration” and deceleration” in temperature ramp rates that arenecessary to heat or cool under these idealized requirements.Temperature acceleration or deceleration is the second time derivativeof temperature. Just as for positional acceleration and deceleration ofa mass at rest, the temperature acceleration and deceleration ratescannot be infinite.

[0005] When heating or cooling from one temperature to another within afurnace, such as a semiconductor wafer processing system, it is oftenimportant to reach the desired setpoint temperature in a minimum amountof time. Classically, a furnace will use a controlled linear ramp to gofrom one temperature setpoint to another. Linear ramping is plagued bytwo disadvantages: a delay in attainment of the desired temperature ramprate by the substrate being heated; and a tendency for the temperatureof the substrate to overshoot the desired setpoint and then oscillatearound the set point temperature before achieving a steady statetemperature. A solution to this problem employing physically attainabletemperature ramp rate acceleration and deceleration phases is describedin copending U.S. patent application Ser. No. 10/068,127, the text ofwhich is incorporated herein by reference.

[0006] Of additional importance is limiting the maximum temperature ramprate to protect against negative thermal effects on the object orobjects being heated due to excessive internal temperature gradientswithin the object. This is of particular concern in semiconductor waferprocessing systems in which important manufacturing aspects are thetemperature variations and values that the semiconductor wafers aresubjected to during processing. In particular, the temperaturedifference between the center and the edge of the wafer duringprocessing in a rapid thermal processing furnace or other similarequipment is of significant interest since excessive heating or coolingof the edge of a wafer relative to its center can result in physicaland/or chemical damage that could render the wafer unuseable or lead toearly failure of semiconductor chips manufactured from the wafer. Thisedge-center temperature difference is referred to as the radial deltatemperature, or radial delta-T (RDT). The problem particularly affectsbatch furnaces, which apply heat to the outside edge of a stack ofwafers. During heating with a radiative heat source such as a resistiveheating coil or a heat lamp, the wafer edges may, at times, be severaldegrees (or even tens of degrees) hotter than the center of the waferbecause radiative heat transfer is greatest at the wafer edges.Conversely, during cooling, the edges undergo more rapid heat lossthrough radiative cooling and thus may be substantially cooler than thewafer centers. At high temperatures, this RDT may induce crystal slip onthe wafer.

[0007] The advantages of limiting temperature ramp rates to minimizethermal expansion stress induced crystal slip damage on semiconductorsubstrates is well known. It is desirable to minimize the RDT duringprocessing to minimize excess thermal stress occurring on the substrate.The temperature ramp rate during processing is the primary factor indetermining the RDT. At higher ramp rates, the thermal inertia of asubstrate being heated can further exacerbate the temperature variationsbetween its edge and its center as heat applied to the edges is notinstantaneously conducted to the center of the substrate. At lowertemperatures, a larger RDT can be tolerated without causing excessthermal stress because silicon atom-to-atom bonds are stronger and canwithstand more thermal stress at lower temperatures. Thus, it isdesirable to provide a system and method for the control of RDT across asubstrate. To avoid exceeding the maximum allowable thermal stress on awafer, prior art methods rely on manually programmed sequences of fixedramp rates. This approach prevents the process from functioning at themaximum possible ramp rate throughout a heating or cooling processbecause the actual maximum allowable ramp rate to avoid RDT-inducedthermal stress damage varies with temperature as noted above.Furthermore, this segmented ramp rate profile can also result in ramprates that exceed the allowable maximum RDT for a given temperature.Heating with a noncontinuous temperature ramp profile therefore deviatesfrom the ideal maximum ramp rate curve.

[0008] Accordingly an improved system and method of temperature controlis needed to govern the ramp rate as a function of the temperature of abody or substrate being heated or cooled.

SUMMARY OF THE INVENTION

[0009] It is an object of the present invention to provide an improvedsystem and method for limiting the radial delta temperature on asubstrate as it is heated by controlling the temperature ramp rateduring processing. Specifically, the present invention provides a systemand method of controlling the radial delta temperature (RDT) across asubstrate by using a dynamically variable temperature ramp rate. Ingeneral, the temperature ramp rate is reduced as the temperature of thebody increases. More particularly, the present invention provides animproved system and method of controlling the radial delta temperatureoccurring as a substrate is heated in a manufacturing process, such asbut not limited to semiconductor wafer processing and equipment.

[0010] One embodiment of the present invention provides a method oflimiting the rate at which a variable is ramped. A maximum allowableramp rate of the variable is calculated at the current setpoint value ofthe variable. The variable is ramped at no greater than this maximumallowable ramp rate until the next setpoint value of the variable undercontrol is reached.

[0011] In another embodiment of the present invention, a method isprovided for changing the temperature of a body housed in a heatingchamber of a temperature controlled furnace from a starting temperatureto an ending temperature using a temperature control algorithm.Temperature data from one or more temperature sensing devices in theheating chamber and a temperature set point are provided as inputs tothe temperature control algorithm which controls power delivery to oneor more controllable heating elements in the furnace. A maximumallowable temperature ramp rate is calculated as a function of thesetpoint temperature. The temperature set point is accelerated from thestarting temperature at a finite acceleration rate until the calculatedmaximum allowable temperature ramp rate for the current temperaturesetpoint is achieved. The temperature set point is decelerated at afinite deceleration rate until the ending temperature is reached suchthat the temperature of the body reaches the ending set pointtemperature smoothly without substantially overshooting or oscillatingabout the ending temperature.

[0012] Additional embodiments of the present invention provide a furnacewhich changes the temperature of a body inside the furnace according tothe methods summarized above.

[0013] These methods are applicable to a variety of systems requiringprecise control of process variables such as temperature set points, gasflow rates, concentrations, pressures, tension, voltage, applied force,and position. In one illustrative embodiment, the system and method ofthe present invention is carried out in a multi-zone furnace used insemiconductor processing.

BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Other objects and advantages of the present invention will becomeapparent upon reading the detailed description of the invention and theappended claims provided below, and upon reference to the drawings, inwhich:

[0015]FIG. 1 is a simplified diagram of one example of a furnace used insemiconductor manufacturing which may employ the system and method ofthe present invention.

[0016]FIG. 2 is a chart of the maximum radial delta temperature vs. thewafer edge temperature for a silicon substrate obtained from Equation 1.

[0017]FIG. 3 is a flow chart illustrating one embodiment of the methodof the present invention.

[0018]FIG. 4 is a graph showing: (i) the ramped setpoint, and (ii) thewafer temperature weighted average for all zones.

[0019]FIG. 5 is a graph showing: (i) the actual center and edgetemperatures for all zones; (ii) the RDT value for all zones; and (iii)the furnace power for each zone over time according to one embodiment ofthe present invention.

[0020]FIG. 6 is a graph illustrating: (i) the weighted average of thecenter and edge temperature (⅔ edge+⅓ center) on a semiconductorsubstrate wafer, which is normally used to represent the overall wafertemperature; (ii) the RDT value for all zones; and (iii) the furnacepower for each zone over time according to one embodiment of the presentinvention.

[0021]FIG. 7 is a graph: (i) showing a close up of the top of the wafertemperature profiles shown in FIG. 5, and (ii) displaying the weightedaverage for all zones according to one embodiment of the presentinvention.

[0022]FIG. 8 is a graph showing: (i) the actual wafer center and edgetemperatures for all zones for the 5, 10, 15 & 20 deg. C. min⁻¹temperature ramp rates; (ii) the RDT value for each zone for each ramprate; and (iii) the furnace power for each zone for each ramp rate overtime for ramping without the RDT control method of the presentinvention.

DETAILED DESCRIPTION OF THE INVENTION

[0023] As described above, it is desirable to minimize the radial deltatemperature or RDT across a body such as, for instance, a semiconductorsubstrate or wafer, to avoid the occurrence of excess thermal stress orcrystal “slip” on the body. The method of the present invention is alsogenerically applicable to any process in which the maximum ramp rate ofa control variable is limited to minimize stress in a system. Accordingto one embodiment of the present invention, RDT is maintained below theexcess thermal stress curve by controlling the temperature ramp rate.This curve of maximum allowable thermal stress is a function oftemperature. The present invention provides that the maximum temperatureramp rate varies with temperature to maintain the excess thermal stresscurve below the maximum allowable value for the current temperature ofthe body being heated.

[0024] At lower temperatures, a body such as a semiconductor wafer isless susceptible to RDT induced excess thermal stress damage than it isat higher temperatures. Since the ramp rate of temperature in a furnace(such as that shown in FIG. 1) is the primary driving factor determiningRDT, the RDT on a body being heated or cooled in a furnace is controlledby limiting the maximum allowable temperature ramp rate as a function ofthe current temperature in the furnace. At lower temperatures, the ramprate is permitted to be greater. The ramp rate is gradually reduced asthe temperature rises. This gradual reduction in the temperature ramprate produces a substantially smooth, continuous temperature curve as afunction of time. In this manner, the present invention provides for avariable maximum allowable temperature ramp rate. By controlling theramp rate and RDT in this way, the present invention minimizes theamount of time required to ramp the body or substrate from onetemperature to another without causing undue stress or damage to thesubstrate.

[0025] In one embodiment of the present invention, a method is providedfor limiting the maximum ramp rate at which a controlvariable—temperature in this example—is increased or decreased. Theinvention may be carried out on a semiconductor furnace as illustratedin FIG. 1. The furnace 10 in FIG. 1 include a heater element 12 havingfive separate zones 14, and a heating chamber 16 housing one or moresemiconductor substrate wafers 20. A power command or signal 22 isindividually controlled in each zone 14. The purpose of the heaterelement 12 is to heat the wafers 20 to a desired temperature 24. Atemperature controller 26 having temperature control software 30 andprocess control software 32 sends the power command signal 22 to thefurnace heater element 12. While a specific semiconductor furnace 10having five zones 14 is shown, it will be understood by those of skillin the art that the system and method of the present invention can beemployed in other types of furnaces, and further can be carried out inother types of semiconductor equipment or other apparatuses designed tocontrollably change the temperature of a body or object from onesetpoint temperature to another. The invention is not limited to thespecific examples shown. For example, the invention may be used in afurnace with a different number of zones. Likewise, it may be applied toany other process or system in which stresses may be controlled bylimiting the ramp rate of a control variable as a function of thatvariable. Additionally, the method may be applied to control stress bylimiting the ramp rate of one or more variables as a function of thoseone or more variables.

[0026] In one embodiment of the present invention, the temperaturecontroller 26 contains temperature control software 30 such as, forinstance PID control software configured to maintain control of thefurnace 10. The ramping of the set point changes depending on thetemperature and final setpoint, and is curved during ramping. Morespecifically, the ramp rate is the slope of the set point temperature.Since semiconductor substrates tolerate higher RDT without experiencingthermal expansion damage at lower temperatures (typically less than 600°C.) than at elevated temperatures (such as in the range of approximately600° C. to 1200° C.), the present invention is configured to startramping the set point more rapidly while the temperatures are relativelylow. As the temperature rises, the maximum tolerable RDT decreases, sothe ramp rate slows as the temperature increases. The higher thetemperature of the substrate or wafer, the slower the ramp rate that isused. The present invention dynamically varies the maximum ramp rate asa function of the current set point temperature. This maximum ramp ratemay be derived from a look up table of maximum allowable RDT as afunction of temperature or from some other programmed function thatprovides a maximum ramp rate as a function of temperature. An example ofsuch a lookup table is provided in Table 1. At temperatures between thetabulated values, the maximum allowable RDT is interpolated for asmoothly varying maximum allowable RDT as a function of temperature. Anexperimentally determined scaling factor is used to convert the maximumallowable RDT to a maximum temperature ramp rate. This scaling factorcan be a constant or it can also itself be a function of temperature.For 300 mm wafers, the scaling factor is preferably 0.5° C. per minuteper ° C. of RDT. Different ramp rate tables may be used, so softwareimplementing the present invention is preferably configured to allowthese ramp rate tables to be selected in the process recipe.Alternatively, the relationship between temperature and maximum ramprate may be programmed as a series of one or more mathematical functionsof temperature. The maximum allowable ramp rate vs. temperature functionis predetermined through experimentation which yield the followingequation for maximum ΔT as a function of temperature: $\begin{matrix}{{\Delta \quad T} = {\frac{2}{{.4928}\quad \alpha \quad E}C\frac{f\quad ɛ^{\frac{1}{n}}}{f\quad t}^{(\frac{U}{nkT})}}} & (1)\end{matrix}$

[0027] where ƒε/ƒt is the strain rate, E is Young's modulus (E=1.9×10¹¹N m⁻²), α is the coefficient of thermal expansion of the substrate (inthis case silicon), C and n are numerical constants (C=4.5×10⁴ N m⁻² andn=2.9), k is Boltzmann's constant (k=1.38×10⁻²³ J K⁻¹) and T is theabsolute temperature of the edge of the substrate where the thermalgradients are presumed to be the highest. The equation is independent ofradius and thus applies to any size substrate. The results of thismaximum calculated ΔT are shown in FIG. 2. TABLE 1 Maximum ramp ratelook up table Temperature set point, ° C. Maximum Allowable RDT, ° C.600 80 700 60 800 44 900 34 1000 26 1100 22 1200 18

[0028] More specifically, one embodiment of the method of the presentinvention is illustrated in FIG. 3. FIG. 3 is a flow chart illustratingone embodiment of the method of the present invention. The method startsat step 40 and a ramping inquiry is made at step 42. If the decision isno, the previous setpoint is used at step 44. If the decision is yes,the inquiry is made whether it is time to start decelerating the ramprate at step 46. If the decision at step 46 is yes, the methodcalculates the deceleration rate at step 48. If the decision at step 46is no, the algorithm verifies whether the ramp rate is currentlydecelerating. If the ramp rate is decelerating at step 50, then thesetpoint is calculated based on the deceleration rate at step 32 and themethod is done (step 54). If the ramp rate is found to be notdecelerating at step 50, the maximum RDT for the current temperature isdetermined by a table lookup and interpolation if necessary at step 56.Also at step 56, the maximum RDT value returned from the table lookup isconverted to a maximum ramp rate using a scaling factor.

[0029] Next, the inquiry is made whether the ramp rate is below themaximum ramp rate at step 58. If no, the maximum ramp rate is used tocalculate the new setpoint at step 60. If yes, then the ramp rate isaccelerated up toward the maximum ramp rate at step 62.

[0030] An illustrative implementation of the resulting curved set pointis shown graphically in FIG. 4. In practice this embodiment of thepresent invention may be implemented through the following conceptualsteps: a maximum allowable temperature ramp rate is calculated asdescribed above for the current set point temperature and the setpointtemperature is ramped at a rate that does not exceed this maximumallowable ramp rate.

[0031] In accordance with a further embodiment of the present invention,the temperature set points are curved while increasing or acceleratingthe ramp rate from zero at the starting temperature to the maximum ramprate and then again while decreasing or decelerating the ramp from themaximum ramp rate back to zero at the ending temperature to providesmooth transitions between steady state (zero ramp rate) and rampingphases of the heating or cooling process. The ramp rate is acceleratedup to the maximum, and decelerated down to the final set point at afinite and physically attainable rate to minimize oscillations of theactual body temperature relative to the setpoint temperature. In apreferred embodiment of the present invention, the temperature ramp isaccelerated and decelerated at a linear acceleration and decelerationrate (the second derivative of the temperature setpoint with regards totime is a constant). However, nonlinear deceleration may be preferredunder some conditions.

[0032] The setpoint ramp rate fed to the temperature controller followsthe lesser of a) the maximum allowable ramp rate temperature curveobtained dynamically from the RDT vs. temperature table and the scalingfactor for the current setpoint temperature, b) the ramp rate providedby the setpoint curve, and c) the maximum ramp rate attainable by thefurnace until the set point temperature approaches the final setpoint.Then the setpoint ramp rate is decelerated smoothly to meet the finalending temperature. The method of the present invention delivers thewafers to the desired temperature at the fastest possible rate thatkeeps the RDT below the slip curve.

[0033] In this embodiment, preferably two sets of thermocouples: one ormore spike thermocouples 34 and one or more profile thermocouples 36,are used for temperature measurement as shown in FIG. 1. The spikethermocouples 34 are closer to the heater element windings (not shown),and respond faster to control inputs. The profile thermocouples 36 arecloser to the wafers 20, and thus better represent their temperature.Temperature controller 26 having temperature control software 30receives the desired temperature 24 set point from process controller 32having process control software, and reads the measured temperatures 38of the thermocouples. The measured temperatures 38 are combinedmathematically to generate a control temperature (not shown) thatprovides an estimate of the temperature of the wafers 20. The controltemperature is preferably a weighted average of the temperaturesmeasured by the spike thermocouples 34 and the profile thermocouples 36.The weighting may preferentially vary as a function of temperature witthe spike thermocouple 34 temperatures being weighted more strongly athigher temperatures. In a further preferred embodiment, the mathematicalcombination of the measured temperatures 38 also includes one or moretemperature offsets. These offsets can be static or dynamic. In oneexample, static offsets are employed to correct the control temperaturefor differences between the temperature of the wafers or other bodybeing heated and the thermocouple temperatures. These offsets may bedetermined experimentally using thermocouple instrumented wafers. Basedon the control algorithm and the inputted control and setpointtemperatures, the temperature controller 26 determines the amount ofpower to apply to each zone of the furnace heater element 12.

[0034] When a ramp rate is specified, the setpoint will ramp at theselected rate. In a preferred embodiment, the setpoint curves smoothlyto the final setpoint near the end of the setpoint ramp phase. Duringthe time that the setpoint curves toward the final setpoint, the ramprate decelerates linearly. This curving of the programmed temperaturesetpoint is preferentially employed at the end of the ramp. However, itis also advantageously applied to the beginning of the ramp to avoidlarge oscillations in power demand.

[0035] When ramping under the method of the present invention at themaximum temperature ramp rate, the instantaneous temperature setpointdoes not jump immediately to the final setpoint as in commonly employedtemperature controllers such as PID systems. Instead, the setpoint isaccelerated at a finite and physically attainable rate until it reacheseither the maximum attainable ramp rate for that zone and setpoint, orthe maximum allowable ramp rate for the current temperature obtainedfrom the product of the maximum allowable RDT for the current setpointtemperature from Table 1 and the scaling factor. The maximum allowabletemperature ramp rate as a function of the current setpoint temperatureis obtained in real time from the product of a Radial Delta-T vs.temperature function and a scaling factor. The RDT vs. temperaturefunction is provided as a mathematical relationship, or in a lookuptable as described in the preceding embodiment. If a lookup table isused, the software is configured to interpolate the maximum allowableRDT at temperatures for which a tabulated value is not provided. Thescaling factor used to convert maximum allowable RDT at a giventemperature to a maximum allowable ramp rate as a function oftemperature may be constant or may itself also be a function oftemperature.

[0036] A system is also provided in an additional embodiment wherein themethod of the present invention is used to control the ramp rate of thesetpoint temperature in a temperature controlled furnace.

[0037] In another embodiment, a system is provided wherein the method ofthe present invention is combined with the temperature control methoddescribed in copending U.S. patent application Ser. No. 10/068,127, thedisclosure of which is hereby incorporated by reference in its entirety.

EXPERIMENTAL

[0038] Several tests was performed with the system and method of thepresent invention using a furnace similar to that shown in FIG. 1 andemploying thermocouple instrumented wafers (semiconductor wafers withembedded thermocouples that provide temperature data for differentregions of the wafer). FIGS. 4 to 7 show thermocouple instrumented wafertemperature data and furnace power delivery for an illustrativeexperiment in which the temperature ramp rate is accelerated anddecelerated linearly and the maximum ramp rate is controlled to maintainthe RDT below the maximum allowable thermal stress curve. A thermocoupleinstrumented wafer is heated from 600° C. to 950° C. under theseconditions. FIG. 5 is a graph of data collected in this experimentshowing: (i) the actual center and edge temperatures for all zones; (ii)the RDT value for all zones; and (iii) the furnace power for each zoneover time. FIG. 6(i) shows the weighted average of the center and edgetemperature (⅔ edge+⅓ center) on the thermocouple instrumented wafer inthis experiment, and FIG. 7 shows a close up of the top of the ramp inFIG. 5, and the weighted average for all zones.

[0039] In another experiment, the system and method of the presentinvention was carried out in a Rapid Vertical Processing (RVP) typefurnace having five zones as shown in FIG. 1. FIG. 4 shows the rampedsetpoint, plus the measured wafer temperature weighted average for allzones. This plot demonstrates how well the actual wafer temperaturesconform to the temperature setpoint curves.

[0040]FIG. 8 shows the results of a linear ramp test in which the ramprate is not controlled by the present invention. The setpoint is rampedlinearly, except that it is curved at the top of the ramp. FIG. 8 showsthe actual wafer center and edge temperatures for all zones for thefollowing ramp rates: 5, 10, 15 & 20 deg. C. min⁻¹. Section (ii) of FIG.8 shows RDT for the wafer and section (iii) shows the applied power as afunction of time. As FIG. 8 shows, increasing the ramp rate in theabsence of RDT-based ramp rate control leads to dramatically greater RDTvalues than were observed in FIGS. 4 and 5 in which the method of thepresent invention was employed.

[0041] The system and method of the present invention provides desirableperformance. The foregoing description of specific embodiments andexamples of the invention have been presented for the purpose ofillustration and description, and although the invention has beenillustrated by certain of the preceding examples, it is not to beconstrued as being limited thereby. They are not intended to beexhaustive or to limit the invention to the precise forms disclosed, andobviously many modifications, embodiments, and variations are possiblein light of the above teaching. It is intended that the scope of theinvention encompass the generic area as herein disclosed, and by theclaims appended hereto and

What is claimed is:
 1. A method of limiting the rate at which a variableis ramped, comprising the steps of: calculating a maximum allowable ramprate of said variable at the current value of said variable; andlimiting the rate at which said variable is ramped such that is does notexceed said maximum allowable ramp rate.
 2. The method of claim 1wherein said variable is a setpoint temperature of a body being heated.3. The method of claim 2 wherein said body being heated is one or moresemiconductor substrates.
 4. The method of claim 3 wherein said maximumallowable ramp rate is a function of a maximum radial delta temperatureon a wafer at the current temperature.
 5. A method of changing thetemperature of a body housed in a heating chamber of a temperaturecontrolled furnace from a starting temperature to an ending temperatureusing a temperature control algorithm comprising the steps of: providingtemperature data from one or more temperature sensing devices in saidheating chamber and a temperature set point as inputs to saidtemperature control algorithm which controls power delivery to one ormore controllable heating elements in said furnace; calculating amaximum allowable temperature ramp rate as a function of temperature;accelerating said temperature set point from said starting temperatureat a finite acceleration rate until said maximum allowable temperatureramp rate for the current temperature setpoint value is achieved; anddecelerating said temperature set point at a finite deceleration rateuntil said ending temperature is reached such that the temperature ofsaid body reaches said ending set point temperature smoothly withoutsubstantially overshooting or oscillating about said ending temperature.6. The method according to claim 5 wherein said controllable heatingelements are selected from the group consisting of radiant heat lampsand heating coils.
 7. The method according to claim 5 wherein saidtemperature sensing devices are one or more thermocouples providing oneor more temperatures for each of said one or more controllable heatingelements.
 8. The method according to claim 7 wherein a controltemperature which is a mathematical combination of said one or morethermocouple temperatures is an input to said temperature controlalgorithm.
 9. The method according to claim 8 wherein said controltemperature is further defined to have a known offset from saidthermocouple temperatures.
 10. The method according to claim 9 whereinsaid temperature offsets are static offsets that correct said controltemperature for differences between the temperature of said body andsaid thermocouple temperatures.
 11. The method according to claim 5wherein said body is a semiconductor substrate.
 12. A temperaturecontrolled furnace for changing the temperature of a body comprising: aheating chamber housing one or more controllable heating elements, andone or more temperature sensing devices; and a temperature controllerconfigured to carry out the method of claim
 1. 13. A temperaturecontrolled furnace for changing the temperature of a body comprising: aheating chamber housing one or more controllable heating elements, andone or more temperature sensing devices; and a temperature controllerconfigured to carry out the method of claim 5.